The Lorentz Invariant Measure and the Heisenberg Uncertainty Principle
A novel approach to the Heisenberg Uncertainty Principle is presented in this paper in a fashion that directly links Special Relativity and Quantum Theory from first principles.
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The traditional approach to non-relativistic quantum mechanics is primarily didactic. The basic axioms of the theory are introduced, along with the Heisenberg Uncertainty Principle and simple systems like the Quantum Harmonic Oscillator are elucidated.
A different approach, which is heuristic in nature, is to begin with the Lorentz Invariant Measure from Special Relativity. The Lorentz Invariant Measure can be used as a conceptual foundation of quantum mechanics, and as a direct link between special relativity and Quantum Theory without recourse to subsidiary conditions.
As a result of this heuristic approach, a foundation can be laid that firmly joins the two fields, which are typically elucidated separately, until either second quantization or the Klein-Gordon and Dirac equations are presented.
(p.s. Alicia has asked me to take her name off this article. While she had a chance to preview the article and discuss its content with the primary author, Alicia feels that she did not contribute sufficiently to warrant being a coauthor of this paper.)